Finite Group Databasebeta

← Prev (#14285476) Next (#14285478) →

C3×D5×#334 #14285477

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×D5×#334

Splittings

FittingC3×C5×#334 ⋊ C2
HallC3×C5 ⋊ C2×#334
SylowC5 ⋊ C2×C3×#334

Subgroups

subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C22×C3×C8
FrattiniC42C22×C3×D5
FittingC3×C5×#334C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C4⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#334D5
hypocenterC5C2×C3×#334
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×#334

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11175);